How to cut line in a face without Knife?
Knife should work for this:



I suspect the darker face on the right is the result of a second, super-imposed face which is preventing the knife tool from working. To fix it, delete the face or use W> Remove Doubles:



That said, there might be a faster way to get the desired result, for example Subdivide and Bevel:



I also used triangulate (&#9096; CtrlT) at the end; not sure if those diagonal edges were desired or not.